kaylasword5013 kaylasword5013

27-12-2023
Mathematics

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Show that the following are equivalent metrics for Rn: (i) d1 (x, y) = || x – y ||1 = nΣi=1 (xi – yi)2(1/2); (ii) d2 (x, y) = || x – y ||2 = max1 ≤ i ≤ n |xi – yi|; (iii) d3 (x, y) = || x – y ||3 = nΣi=1 |xi – yi|.

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